This note is concerned with the Cauchy problem for hyperbolic systems of conservation laws in several space dimensions. We first discuss an example of ill-posedness, for a special system having a radial symmetry property. Some conjectures are formulated, on the compactness of the set of flow maps generated by vector fields with bounded variation.
@article{RLIN_2004_9_15_3-4_225_0, author = {Alberto Bressan}, title = {Some remarks on multidimensional systems of conservation laws}, journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni}, volume = {15}, year = {2004}, pages = {225-233}, zbl = {1162.35412}, mrnumber = {2148881}, language = {en}, url = {http://dml.mathdoc.fr/item/RLIN_2004_9_15_3-4_225_0} }
Bressan, Alberto. Some remarks on multidimensional systems of conservation laws. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 15 (2004) pp. 225-233. http://gdmltest.u-ga.fr/item/RLIN_2004_9_15_3-4_225_0/
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